A sum of 2709 is to be given in the form 63 prizes. If the prize of either 100 or 25, find the number of prizes given each type

The optimal values of w and visualize the training samples and the corresponding polynomial functions for different degrees of n.

To solve the given task of finding the optimal values of w for a polynomial h(x,w) that minimizes the squared error objective function L, we can follow the provided procedure. Here is a step-by-step guide:

Step 1: Derive the formula for the gradient of L with respect to w as a function of the training sample values x and y. This involves calculating the vector of partial derivatives of L with respect to each coefficient wj.

Step 2: Initialize the values of wj with small random values in the range [-0.001, 0.001].

Step 3: Calculate the gradient g(x,y) for each training point (x,y) and average them to obtain g.

Step 4: Update the values of w by subtracting a small positive number q times g, i.e., w_new = w_old - q * g.

Step 5: Repeat steps 3 and 4 until the quality of predictions, measured by the squared error objective function, no longer significantly changes. This may require thousands of iterations.

Step 6: Once the optimal values of w are obtained, plot the training samples as red points on an x-y plot, using a horizontal axis range of -2.5 to 2.5.

Step 7: Plot the function h(x,w) as a blue curve on the same plot, by evaluating it for various values of x within the range -2.5 to 2.5. Use a scatter plot without connecting lines.

Step 8: Repeat the above steps for different values of n, starting from n = 1 to n = 5, creating separate plots for each value of n.

By following this procedure, you will be able to find the optimal values of w and visualize the training samples and the corresponding polynomial functions for different degrees of n.

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Answer:

25

Step-by-step explanation:

"Spongebob reference" Well really its 24* and the only right answer to this is 25

Answer:

Because the points can often represent something, i.e if you used quadratics to model say the area of something, calibrating the turning point, will give you the given length needed for the dimension of that, plus the maximum area those dimensions can yield.

Step-by-step explanation:

Answer:

height of the building = 36√3 m

Step-by-step explanation:

Answer:

62.4 m

Step-by-step explanation:

           |\----------------------------------------

           |    \   60°

           |        \

   h      |            \

           |                \

           |           60°    \

           ---------------------  A

                    36 m

Point A is 36 m from the foot of the building. The angle of depression above is 60°. m<A = 60°.

tan A = opp/adj

tan 60° = h/(36 m)

h = 36 * tan 60° m

h = 62.4 m

Answer: 62.4 m

Answer:

2x3(x+5)(x−5)

Step-by-step explanation:

2x(x as in letter)

Answer:

2x^3(x+5)(x-5)

Step-by-step explanation:

Since both terms are perfect squares, we can solve using difference of squares:

\(2x^5-50x^3\\2x^3(x+5)(x-5)\)

Answer:

37.68 inches

Step-by-step explanation:

The equation for the circumference of the circle is:

\(C=2\pi r\)

We can substitute 6 in for "r" and 3.14 for "π":

\(C=2(3.14)(6\ in)\\C=12\ in(3.14)\\C=37.68\ in^\)

Answer:

e.

Step-by-step explanation:

hope this helps

Answer:

The answer is

The first one, the second one and the last one.

Hope this helps.

Answer:

picture

Step-by-step explanation:

The partial derivatives of the original function f(x,y) = 6x3 − 9xy3 with respect to x and y can be found by taking the derivative of the original function with respect to one variable while holding the other variable constant.

The original function is given as f(x,y) = 6x3 − 9xy3. The partial derivatives with respect to x and y can be found by taking the derivative of the original function with respect to one variable while holding the other variable constant.

The partial derivative with respect to x is found by taking the derivative of the original function with respect to x while holding y constant:

∂f/∂x = 18x2 - 9y3

The partial derivative with respect to y is found by taking the derivative of the original function with respect to y while holding x constant:

∂f/∂y = -27xy2

Therefore, the partial derivatives of the original function f(x,y) = 6x3 − 9xy3 with respect to x and y are ∂f/∂x = 18x2 - 9y3 and ∂f/∂y = -27xy2, respectively.

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Answer:

18.94

Step-by-step explanation:

The average thickness of a page in the book= is 0.00393cm

determining the thickness of a page

One page has a thickness of 0.12 mm. Therefore, it's easy; all you have to do is add up the pages and divide that number by two. Then double that result by a page's thickness.

A book has 764 pages in total, including the final page.

3.0 cm is how thick the book is.

Divide across 764 to find the thickness of a page from the book: 3.0/764 = 0.003926701

which is roughly equal to 0.00393 cm

Consequently, 0.00393 cm is the average thickness of a book page.

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This integral represents the sum of the volumes of all the infinitesimally thin cylindrical shells that make up the solid.

To set up the integral for the volume of the solid obtained by rotating the region bounded by the curves y = x, y = 0, and x = 4 about the line x = 8, we can use the method of cylindrical shells.

First, let's draw a rough sketch of the region and the axis of rotation:

```

|

|

|       +-----------+

|       |           |

|       |           |

|       |           |

|       |           |

|       +-----------+ <-- x = 4

|       |

|       |

|       |

|       |

|       |

|       |

|       |

|       |

+------------------------ <-- x = 8

```

The region bounded by y = x, y = 0, and x = 4 is a triangle with a right angle at the origin.

To set up the integral, we consider an infinitesimally thin cylindrical shell with radius r, height h, and thickness Δy. The volume of this shell can be approximated as the product of its circumference, height, and thickness.

The radius of the shell, r, is the distance from the axis of rotation (x = 8) to the curve y = x. Since x = y for the region, r = 8 - y.

The height of the shell, h, is the difference between the x-values at the top and bottom of the region. In this case, h = 4 - 0 = 4.

The thickness of the shell, Δy, represents an infinitesimally small change in the y-direction.

Therefore, the volume of the shell is approximately given by V_shell = 2πr * h * Δy.

To find the total volume, we integrate this expression over the range of y-values that span the region. In this case, the integral is set up as follows:

∫[0, 4] 2π(8 - y) * 4 * dy

This integral represents the sum of the volumes of all the infinitesimally thin cylindrical shells that make up the solid. By evaluating this integral, you can find the exact volume of the solid obtained by rotating the region bounded by y = x, y = 0, and x = 4 about the line x = 8.

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Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x, y = 0, X = 4; about x = 8 2 (8 - y2)2 – 16 dy 0

Since Zx and Zy are suplementary angles, Zx is 92°.

Supplementary angles are 2 angles that if added together created a sum of 180°. Supplementary angles have several properties such:

Supplementary angles might come in adjacent and non-adjacent types. Adjacent supplementary angles share a common arm and a common vertex. The adjacent supplementary angles share one common line segment. Non-adjacent supplementary angles do not have a common arm and vertex. They do not share a common line segment with each other.

On the case, we know that:

Zy = 88°

Zy and Zx --> supplementary angles

Then:

Zy + Zx = 180°

88° + Zx = 180°

Zx = 92°

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Given data:

The list and the measurment of ingredients used to make 16 brownies is as follows.

Butter = 2/3 cups.

unsweetended choclolate = 5 ounces.

sugar = 1 1/2

vanilla = 2 tablespoons.

egg = 2

flour = 1 cup

to find the recipe, ingredients used to make 8 brownies.

Reduce the measure by half,. that is dividing it by 2.

thus,

Butter =1/3

unsweetended choclolate= 2.5 ounces

sugar = 3/4 cup

vanilla = 1 tablespoon.

egg =1

flour= 1/2 cup.

Principal: $400

Interest accrued: $1,311.48 * (10.1% / 12)

Payment (on due date): $400

To get started, let's first determine which card is the higher-interest card. In this case, the Bee4 card has a higher APR of 10.1% compared to the MarK2 card with an APR of 6.5%.

Now, let's focus on the higher-interest card and fill in the table for the first month (Month 1):

Higher-Interest Card (Bee4) - Payoff Option

Month 1

Principal: This is the portion of the payment that goes towards reducing the balance. Since you're paying only the interest on the lower-interest card, the full $400 payment will go towards the principal of the higher-interest card.

Interest accrued: Calculate the interest accrued on the existing balance of the higher-interest card. To do this, multiply the existing balance by the monthly interest rate (10.1% divided by 12).

Payment (on due date): This is the total payment you'll make towards the higher-interest card, which is $400.

End-of-month balance: Subtract the principal payment from the existing balance and add the interest accrued to get the new balance.

Using the given information:

Existing balance: $1,311.48

Monthly interest rate: 10.1% / 12

Principal: $400

Interest accrued: $1,311.48 * (10.1% / 12)

Payment (on due date): $400

End-of-month balance: Existing balance - Principal + Interest accrued

Once you've calculated these values for the first month, you can continue filling out the table for the subsequent months using the same logic, adjusting the existing balance and interest accrued based on the previous month's values.

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The ordered pairs that correspond to input-output pairs for the given function are (3, 24) and (-2, 30).

To find these ordered pairs, we simply substitute the given values of X into the function y = -2X + 30 to obtain the corresponding value of Y, which represents the number of gallons of water remaining in the bathtub after X minutes of water leakage.

Therefore, when X = 3, Y = -2(3) + 30 = 24, which gives us the ordered pair (3, 24). Similarly, when X = -2, Y = -2(-2) + 30 = 34, which gives us the ordered pair (-2, 30).

The ordered pairs (24, 3), (3, 36), and (15, 0) do not correspond to valid input-output pairs for the given function.

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A polygon is called non-convex if there are "dents" or indentations in it, where the internal angle is greater than 180 degrees.

In other words, a non-convex polygon is a polygon whose line segments intersect, creating an interior angle greater than 180 degrees. This is in contrast to a convex polygon, where all of the interior angles are less than 180 degrees and none of the line segments intersect.

Non-convex polygons can have a variety of shapes and sizes, and can be composed of any number of sides. However, they are generally more difficult to work with mathematically than convex polygons, and often require more advanced techniques to analyze and understand their properties.

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Answer:

7/12 + 2q/3

Step-by-step explanation:

11/12 - 1/3

= 11/12 - 4/12

=(11-4)/12

= 7/12

All the picture:

11/12  - 1q/6 + 5q/6 - 1/3

= 11/12 - 1/3 - 1q/6 + 5q/6

= 7/12 + 4q/6

= 7/12 + 2q/3

Answer:

7-8q/12 is the answer

i aspect that it will be helpful for you

Answer:

yes

Step-by-step explanation:

Derek must give the bank approximately $26,695.78 to pay off his car loan after 11 months. To calculate how much Derek must give the bank to pay off his car loan after 11 months, we need to consider the principal amount borrowed, the interest rate, the loan term, and the number of payments made.

Derek borrows $30,924.00 to buy a car, and he will make monthly payments for 6 years. The interest rate is 5.89%.

First, we need to calculate the monthly interest rate. We divide the annual interest rate by 12 (number of months in a year) and convert it to a decimal:

Monthly interest rate = 5.89% / 12 = 0.4908%

Next, we calculate the number of payments made up to the point when Derek decides to pay off the loan. In this case, he makes payments for 11 months.

Now, let's calculate the remaining balance on the car loan using the formula for the remaining balance on an amortizing loan:

Remaining balance = Principal * [(1 + r)^n - (1 + r)^p] / [(1 + r)^n - 1]

Where:

Principal = $30,924.00 (initial loan amount)

r = Monthly interest rate (0.004908)

n = Total number of payments (6 years * 12 months per year = 72 payments)

p = Payments made (11 payments already)

Substituting the values into the formula, we have:

Remaining balance = $30,924.00 * [(1 + 0.004908)^72 - (1 + 0.004908)^11] / [(1 + 0.004908)^72 - 1]

Using a calculator, we can evaluate this expression:

Remaining balance ≈ $30,924.00 * [1.4042 - 1.0552] / [1.4042 - 1] ≈ $30,924.00 * 0.3490 / 0.4042 ≈ $26,695.78

Therefore, Derek must give the bank approximately $26,695.78 to pay off his car loan after 11 months.

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The limit of the function as the variable n tends to minus infinity is -1. Option C is correct

Given the limit of a function expressed according to the equation;

a(n) = 6n²-n-3n³/3n³+n-1

The value of the function if n tends to minus infinity is expressed as show:

a(n) = 6n²-n-3n³/3n³+n-1

Divide both all the terms by n³

a(n) = 6n²/n³-n/n³-3n³/n³/3n³/n³+n/n³-1/n³

a(n) = 6/n-1/n²-3/(3+1/n²-1/n³)

a(n) = 6/-∞ - 1/(-∞)²-3/(3+1/(-∞)²-1/(-∞)³)

a(n) = -3/3

a(n) = -1

Hence the limit of the function as the variable n tends to minus infinity is -1

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5. We have Angle, Angle and Side to constitute the AAS theorem and prove the triangles are congruent.

6. We have Side, Side and angle not between them so we don't have enough information to prove the congruency of the triangles.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

5. We have Angle, Angle and Side to constitute the AAS theorem and prove the triangles are congruent.

6. We have Side, Side and angle not between them so we don't have enough information to prove the congruency of the triangles.

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\(\text{Given that,}\\\\s_1 = 5.95,\\\\s_2 = 5.42\\\\\\F= \dfrac{(s_1)^2}{(s_2)^2} = \dfrac{(5.95)^2}{(5.42)^2} = 1.21\)

Answer:

  49.2°

Step-by-step explanation:

You want the angle of elevation of the sun if a 695 ft monument casts a 600 ft shadow.

The tangent relation between sides and angles in a right triangle is ...

  Tan = Opposite/Adjacent

In the attached figure, this means ...

  tan(S) = MB/SB

Using the inverse tangent function we find ...

  S = arctan(MB/SB) = arctan(695/600) ≈ 49.2°

The angle of elevation of the sun is about 49.2°.

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Answer:

w^2+9w+20

Step-by-step explanation:

Apply the FOIL METHOD: (a + b) (c + d) = ac + ad + bc + bd

a = 5        

b = w        

c = w            

d = 4

= 5w + 5 x 4 + ww + w x 4

= 5w + 5 x 4 + ww + 4w

Simplify 5w + 5 x 4 + ww + 4w:

w^2 + 9w + 20

Answer:

x=7

Step-by-step explanation:

5(2x-5) = 10x-25

1) add 25 to both sides

10x+25=10x      6x+3+25=6x+28

10x=6x+28

2) subtract 6x from both sides

10x-6x=4x      6x+28-6x=28

4x=28

3) divide by 4 from both sides

4x/4=x      28/4=7

x=7

Hope this helps, have a great day!!

The value of y in the expression -5(2x - 5) = 6x + 3 is 22/16

According to the given question

We have an equation in one variable

⇒  -5(2x - 5) = 6x + 3

For finding the value of x solve the above equation by adding and subtracting the like terms.

So, -5(2x - 5) = 6x + 3

⇒ -5 x 2x + 5 x 5 = 6x + 3

⇒ -10x + 25 = 6x + 3

⇒  25 - 3 = 6x + 10x

⇒  22 = 16x

⇒ x = 22/16

Hence, the value of y in the expression -5(2x - 5) = 6x + 3 is 22/16

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Answer:

-1

Step-by-step explanation:

-1 is 11/12 at its simplest form